Question

Answer

Squaring each side of

\[x - 12 = \sqrt{x + 44}\]

\[(x - 12)^2 = (\sqrt{x + 44})^2 = x + 44\]

\[(x^2 - 24x + 144 = x + 44\]

\[(x^2 - 25x + 100 = 0\]

\[(x - 5)( x - 20) = 0\]

The solutions to the quadratic are x = 5 and x = 20. However, since the first step was to square each side of the given equation, which is not a reversible operation, you need to check x = 5 and x = 20 in the original equation. Substituting 5 for x gives

\[5 - 12 = \sqrt{( 5 + 44)} \]

\[-7 = \sqrt{49} \]

This is not a true statement (since √49 represents only the positive square root, 7), so x =5 isnota real solution to

\[x - 12 = \sqrt{x + 44}\]

Substituting 20 for x gives:

\[20 - 12 = \sqrt{20 + 44}\]

\[8 = \sqrt{64}\]

This is a true statement, so x = 20 is a solution to x − 12 = √(x + 44). Therefore, the solution set is {20}, which is choice B.